If I understand correctly, celadon glaze contains iron oxide. Does it affect the taste of tea in any meaningful way? I don't expect tetsubin-level results, but is it even noticable?

I like the look of it, and consider getting a gaiwan in celadon coated porcelain. A lot of the ones for sale seem to be clay rather then porcelain though, and some are so cheap that I wonder if they just have a similar colour instead of real celadon glaze. What "should" celadon cost in order to be real? Any recommended gaiwans? Or should I just stick with white porcelain?